Modern loudspeaker systems are expected to accurately reproduce sound across the entire audible audio spectrum. No individual speaker element (i.e., driver), however, has been found that can accurately reproduce this entire range of audible frequencies. Therefore, high-fidelity loudspeaker systems are generally realized by dividing the audio frequency spectrum into two or more separate frequency bands and applying each of these bands of the audio frequency range to separate drivers. For this purpose, crossover network filters are provided. Each driver may then be optimized to best reproduce a particular range or band of frequencies. When properly combined into a loudspeaker system, such drivers and an appropriate crossover network form a loudspeaker system capable of more accurately reproducing the entire audible frequency range.
Crossover network filters belong to one of three classes: low-pass for low frequency drivers (i.e., woofers), band-pass for midrange drivers, and high-pass for high frequency (i.e., tweeters).
For perfect fidelity (i.e., accuracy of reproduction of an applied electrical signal), a loudspeaker system is assumed to realize the ideal all-pass transfer function of:f(s)=Ke−sT  (1)where S is the complex frequency variable (s=•+j•), K and T are real positive constants, and e=2.718.
If f(s) represents the acoustic pressure in the space into which the loudspeaker system radiates sound, then Equation (1) defines the transfer function for a perfect loudspeaker system. Such a loudspeaker system has flat amplitude response and linear phase response. To the best knowledge of the present inventor, such a loudspeaker system, having the transfer function defined by Equation (1), has not yet been perfectly realized, at least in a three-dimensional acoustic space using any known method. Accordingly, loudspeaker system configurations have been based on an approximation to this ideal transfer function.
The simplest and probably best-known approximation to the ideal transfer function is illustrated by a two-way loudspeaker system having a single woofer, a single tweeter, and a simple crossover network. Such a loudspeaker system 100 is shown in FIG. 1. A woofer 102 and a tweeter 104 are interconnected by a simple, two-component crossover network 106 having a 6 dB/octave rolloff or slope. The ideal transfer function of Equation (1) may be reduced to one independent of frequency by expanding Equation (1) into a power series.
Setting K=1:
                              f          ⁡                      (            s            )                          =                              ⅇ                          -              sT                                =                      1                          1              +              sT              +                                                                    (                    sT                    )                                    2                                2                            +              Λ                                                          (        2        )            Taking the first term of Equation 2 yields:
                                          f            1                    ⁡                      (            s            )                          =                  1                      (                          1              +              sT                        )                                              (        3        )            
Equation (3) is the transfer function of a circuit having an inductor 110 of T henries in series with a 1 ohm resistor 108, (FIG. 2), which is similar to the woofer-inductor series circuit shown in FIG. 1.
Replacing s with new variable (1/sT) in Equation (1) yields, after expanding and taking the first term as before:
                                          f            2                    ⁡                      (            s            )                          =                              1                          1              +                              1                sT                                              =                      sT                          1              +              sT                                                          (        4        )            
Equation (4) is the transfer function of a circuit having a capacitor 112 of T farads in series with a one-ohm resistor 114, (FIG. 3), which is similar to the tweeter-capacitor series circuit shown in FIG. 1.
If the resistor 108 in FIG. 2 is replaced by an ideal woofer and the resistor 114 in FIG. 3 is replaced by an ideal tweeter, the speaker system in FIG. 1 is obtained. Acoustic output (i.e., sound pressure in the acoustic space) is the sum of woofer and tweeter outputs, which is the sum of equations (2) and (3):
                              Acoustic          ⁢                                          ⁢          Output                =                                            1                              1                +                sT                                      +                          sT                              1                +                sT                                              =          1                                    (        5        )            
Since the sum in Equation (5) is unity (a constant), acoustic output becomes independent of frequency. The speaker system can be considered “perfect,” i.e., having both flat amplitude and linear phase response. While the foregoing analysis shows such a speaker system to be mathematically perfect, problems arise when constructing such a loudspeaker system. First, neither the woofer 102 nor the tweeter 104 exhibit ideal amplitude or phase response. Second, such a loudspeaker system must typically function in a three-dimensional acoustic space in which the simple energy relationship represented by Equation (5) is not valid, at least not for all points in the space.
Third, the gradual crossover filter slopes (i.e., only 6 dB/octave) represented by Equations (2) and (3) allow significant out-of-band energy to enter the drivers (woofer 102 and tweeter 104). This causes low frequency (bass) to overload the tweeter 104. When applied to the woofer 102, high frequency (treble) typically causes cone breakup. This phenomenon causes a variety of distorted sound problems well known to those skilled in the art.
Several solutions to the aforementioned problems have been proposed and/or implemented. One prior art solution was to add sections to the crossover filters. “All pole” transfer functions realized in this way have band-edge slopes of 12, 18, or 24 dB/octave for two, three, or four-section filters, respectively. As crossover filter slopes increase, system performance generally improves. Even a 24 db/octave filter slope, however, has been found to still be insufficient in removing all audible sonic degradations caused by out-of-band signals applied to the drivers. Expansion to more than four filter sections in all pole filter designs has been considered impractical, as many components are required. This typically results in both large power losses as well as excessive cost.
A different approach to loudspeaker crossover filter design is necessary for a practical solution to the aforementioned problems. To understand the infinite slope concept introduced by the instant invention, the so-called brick wall amplitude function is first defined. The brick wall function is illustrated in FIG. 4. In a selected range of frequencies 120 (i.e., the passband) between frequencies f1 and f2, the amplitude response is finite and flat, (i.e., a constant value), while at frequencies 122 (below f1) and frequencies 124 above f2, the amplitude response is zero.
Refer now to FIG. 5 where a second brick wall amplitude function is placed alongside the brick wall function of FIG. 4 in order to increase the range of frequencies covered. FIG. 5 shows two adjacent brick wall amplitude functions with respective passbands 126 and 128 spanning audible frequency range, for example between f1=20 Hz and f3=20 KHz; f2 is a typical crossover frequency, i.e., 2 KHz. The composite brick wall function of FIG. 5, therefore, represents the response of a crossover network having a constant frequency response over the entire audio frequency range. If a perfect woofer and a perfect tweeter were connected to such a crossover network, a loudspeaker system having a flat or constant amplitude response could be realized.
FIG. 7 is a schematic diagram of a simple embodiment 130 of the inventor's infinite slope technology, which provides a crossover filter circuit having an effectively- or quasi-infinite band edge (i.e., greater than 40 dB/octave) frequency response, as shown in FIG. 5. Acoustic outputs of woofer 102 and tweeter 104 are therefore separate and distinct due to the effectively infinite slope at f2, (FIG. 5). Acoustic wave interference between woofer 102 and tweeter 104 is rendered ineffective (i.e., the effects of such interference are reduced to a point of inaudibility) because neither driver 102 nor 104 radiates sound energy in frequencies covered by the other. In other words, drivers on adjacent frequency bands, for example tweeter 104 and woofer 102, effectively operate independently of one another. Distortion is reduced because only negligible bass energy enters and overloads the tweeter 104, and only negligible high frequency energy enters woofer 102 to cause cone breakup.
Until the inventor's infinite slope design was introduced, no useful brick wall loudspeaker crossover filter designs existed that used passive components. Classic filter design techniques available before the introduction of infinite slope were not capable of producing a useful device. Early attempts to design such a network relied on crude, brute force, all-pole filter methods having numerous filter stages. A schematic diagram of one such filter is shown in FIG. 6a. The circuit of FIG. 6a is a low-pass or woofer example and has a useful slope of 96 dB/octave as shown in FIG. 6b. A filter built using the design of FIG. 6a exhibits high signal losses and requires many, typically expensive, components. While the high signal losses may possibly be tolerated, the component cost renders such a circuit generally impractical.
The present inventor's infinite slope method, as disclosed in U.S. Pat. No. 4,771,466 (included by reference), became the first practical, high-slope loudspeaker crossover filter system using all passive components. The disclosed method achieves a steep slope in crossover filter networks using few passive components. Signal loss is small, typically less than 1 dB, so system efficiency is not compromised. Also, because of the low component count, cost is reasonable.
The two-way (i.e., woofer-tweeter), infinite slope speaker system using the inventor's “infinite slope” technology shown in FIG. 7 has only five components in its crossover filter 130—three capacitors 132 and two transformers 134. To explain how the crossover network 130 works, pole-zero concept is utilized. Typically, filter network transfer functions are mathematically characterized as having “poles” and “zeros,” which are the roots of the denominator and numerator polynomials, respectively, of the equation for f(s) (i.e., the transfer function of the crossover network filter). Simply stated, poles indicate output at and near pole frequencies, and zeros indicate no output at or near zero frequencies.
FIG. 8a is a schematic diagram, 136, FIG. 8b is the positive frequency axis poles and zeros (p-z), and FIG. 8c is a typical frequency response plot of a prior art low-pass woofer crossover transfer function. Note that the mirror-image finite p-z on negative frequency axis are not shown. Three zeros are shown at infinity. If, however, a zero could be moved from infinity nearer to the positive frequency pole cluster by simple means, a practical way to increase amplitude function slope would be realized. Note that a mirror image zero would then also move on the negative frequency axis but is not shown. The inventor discovered a new method (i.e., replacing coils L1 138 and L2 140 of FIG. 8a with a transformer) for accomplishing this zero migration. This invention forms the basis for his U.S. Pat. No. 4,771,466 United States Patent filed in 1987 and included herein by reference.
FIG. 8d is a schematic diagram of a simplified circuit utilizing the present inventor's infinite slope technology as described and claimed in U.S. Pat. No. 4,771,466, previously issued to him. For completeness, prior art methods not forming part of the present invention are described in this patent application.
FIG. 8d illustrates a circuit resulting from replacing L1 138 and L2 140 (FIG. 8a) by transformer 142. Note in FIG. 8e that a zero has now appeared on the positive frequency axis close to the pole cluster. This zero, once at infinity (FIG. 8b), becomes finite (FIG. 8e). The transformer 142 (FIG. 8d) moved the zero from infinity to a point close to the pole cluster.
Mathematically, a second, finite, mirror image zero appears on the negative frequency axis (not shown) because zeros always move in pairs from infinity to mirror image positions on finite regions of the frequency axis. This “zero-moving” method produces a good (i.e., effective) approximation to a low-pass brick wall amplitude function (FIG. 8f). Similar methods exist for band-pass and high-pass infinite slope crossover filters. These methods are described in detail in the inventor's '466 patent.
Respectively shown at 144 and 144′ in FIGS. 8c and 8f are slopes in the amplitude response of the low-pass filters in each respective FIGS. 8a and 8d. In FIG. 8c, the slope 144 in response, resulting from the 3-element low-pass filter (FIG. 8a), is 18 dB/octave. In FIG. 8f, the slope 144′ may be as high as 120 dB/octave in the very best embodiments of the invention, which is generally recognized by those skilled in the art as a good or useful approximation to the brick wall amplitude function.
A mutually coupled coil pair or transformer is one method that may be used to generate transfer function transmission zeros in inventor's novel infinite slope circuit. Equations defining some functions of transformers (e.g., transformer 142) used in accordance with the invention are:
                    K        =                  M                                    (                                                L                  1                                *                                  L                  2                                            )                                      1              2                                                          (        6        )                                M        =                              (                          L11              -              L12                        )                    4                                    (        7        )            where:                K=coefficient of coupling;        M=mutual inductance of L1, L2;        L1=self-inductance, primary transformer winding;        L2=self-inductance, secondary transformer winding;        L11=total inductance of L1 and L2 when series-connected with magnetic fields aiding;        L22=total inductance of L1 and L2 when series-connected with magnetic fields opposing.        
Refer now to FIGS. 14a and 14b, which illustrate the well known “T” model for a mutually coupled coil pair or transformer. FIG. 14b shows a transformer 152 in accordance with the model of FIG. 14a. Transmission zeros are generated in accordance with the invention when L1 146 and L2 148 are coupled, causing opposing magnetic fields (not shown); mutual inductance M 150 is shown in transformer model.
Let components assume values:                L1=1 millihenry        L2=1 millihenry        
Then transformer 152 (FIG. 14b) is assembled to yield:                L11=2.4 millihenry        L22=1.8 millihenry        
This gives M a value of 0.15 millihenry from Equation (7), making K equal to 0.15 from Equation (6). This transformer 152 is incorporated into the loudspeaker system crossover of FIG. 10. Amplitude response 154 (FIG. 11) of a midrange driver has slope 156 of at least 40 dB/octave and, in better embodiments of the present invention, up to 120 db/octave.
In the time since the issuance of his '466 patent, the inventor has considered several factors for improving crossover filter networks. Such factors include optimizing the input impedance characteristic of the filter network, and optimizing “acoustic fill” at crossover frequencies.
Inventor's prior art addresses these factors, but it is difficult to simultaneously optimize the factors given above. A new approach is required. After experimentation, a simple solution was found. The inventor's new method combines inventor's prior art with a series-connected “constant resistance” filter network. Also, requirement for infinite slope cutoff at the lower band-edge of some or all filter networks is relaxed. The present inventor's new art permits a better means for simultaneously optimizing both of the factors listed above. In summary, the method of the present invention is described herein relies on several novel steps.
First, at least one series connected, constant resistance network is added at the input terminals of the crossover filter system. In addition, infinite slope designs are used for the upper (higher frequency) band-edge of low-pass and band-pass filters. Optionally, infinite slope designs may be used in the high-pass filters of the network. Also, infinite slope designs may optionally be used for lower band-edge frequencies of band-pass filters.